On a couple recent visits (agency in calls) I've definately had the knock on the door before I have spent the allotted time with the lady.  On one occasion recently  shot two was on the verge (roughly 10 mins left) and the knock happened followed by mamasan pounding at the door two minutes later basically shutting us down.  That is one nut I will never get back.  I think they start the clock when I walk in the door....but the lady doesn't start the fun for 10 minutes as I wait in the room.   I complained, and got 10 extra minutes on a future visit but that hardly helps.  

how do you deal with this?

This probably isn't what you want to hear, but AMP hours are usually scheduled like HS or college class hours.  
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Classes are scheduled at 9 AM, 10 AM, ... 2 PM, 3 PM ...  
To allow travel time between classes (or to allow gents to come and go without bumping into each other), ACTUAL class hours are more like 50 minute hours and class times start at 5-after and end at 5-before the hour.  
9 AM class = 9:05 to 9:55  
10 AM class = 10:05 to 10:55  
(At some places, the class hour is N:00 to N:50 instead of N:05 to N:55 but still a 50 minute hour.)
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I don't think anyone has ever successfully sued a school for only providing 5/6 of the nominal class time. I.e., if a typical college schedule is 40 hours per week for 16 weeks, that's around 12 class "hours" of lecture and 28 hours of reading, homework, and prep time per week and that works out to 12 hours x 16 weeks = an expectation of 192 class "contact hours" (mostly lecture but some class time for quizzes and exams).  
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If you're paying $40,000 per year (2 semesters) for tuition (for a "typical" course load) that's  
($20,000 per semester) / (192 class hours per semester) = $104 per class hour.
If you're only getting 50 minute hours, you are being overcharged by $17 per hour.  
Rather than file a lawsuit, assume that the extra $17 per hour goes to pay for the library, gym, and other amenities (fresh towels, clean sheets, ...).  
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Oh ... back to the AMPs. For simplicity, they try to schedule on the hour: 9, 10, 11, 12, 1, 2 ...
To keep on schedule, each "hour" is a short hour of around 50 minutes or so.  
When the schedule is thrown off enough, the AMPs WILL schedule at a non-N:00 time and tell you to arrive at N:15 or N:30 or whatever but it is still likely to be a "short" hour unless going over gets them back to the N:00 times. I.e., you're told to arrive and ring the bell at 7:40; "start" at 7:45; don't get the knock on the door until 8:50 or 8:55. FULL HOUR!
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The AAMPs (apartment AMPs) are more flexible and the hostesses are more capable of providing a full 60 minute hour.  
The agencies you mention might be strict "50 minute hour" operations but you can ask them if you get a full hour or a 50 minute hour so you'll know ahead of time. But you mention "mamasan" which is more like an AMP.

Discuss the time allocated ahead of the start or ASSUME it's going to be a "short" hour.

I guess you're right about the 50 min sessions when starting on the hour (more or less).  I find the difference between 60 and 50 minutes to be huge as getting a second shot off in 60 is doable and the 50 minutes feels like the gun is at my head.  hope this is the biggest problem in my life.

I left out other details, such as 10-15 minutes for the hostess to clean up herself and the room for the next session. Maybe a more accurate schedule would be:  
1:00 start first appointment  
2:00 end first appointment (happy skidude!)
2:00 - 2:15 hostess preps self and room for next appointment
2:15 start 2nd appointment  
3:15 end 2nd appointment  
and so on for each time slot.
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At the AMPs, the mamasan wants to keep the ball rolling to get in as many gents as possible, including the warning knock and 50 minute hours.
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If you try other options (AAMPs, indies, etc.), you can make a better case for full 60-minute hours. You can try asking for a 1.5 hour = 90 minute = really only 80 minute session at the AMP. It might require scheduling that well in advance or they will have to bump their regulars or other clients. Some phone girls can't do the calculations and will simply say that they have other pre-scheduled appointments at 2:00, 3:00, 4:00 ... and can't fit in the extra half hour for you.

Absolutely! Good luck!

If you start at 2pm and the next guy is coming in at 3pm, you don't get to keep ducking until 3pm. Girl still needs to take you to shower, she needs to clean herself and the room, both of you need to get dressed. That's your 10 minutes. Blame the  massage parlors for not scheduling buffer time.

And yes your time starts when you walk in the door. Why wouldn't it? If the girl is late getting to the room then yeah you should get make up time, but you're paying for the 1hr of time not 1hr of sex.

Or perhaps you would rather the girl show up to your 2pm disheveled with cum on her from her 1pm because she didn't have time to clean up?

If you want a full unrushed hour, you would be better off meeting with indies. They would be less likely to schedule back to back without buffer time. That being said, you should be respectful to the ladies time because if you take 1:15hr, then you're essentially getting time for free from the girl. Make sure she is ok with it.

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Is the second time inclusive?

I feel like the higher end girls arent really clock watchers, and they tend to only see  1 or 2 a week. If you go massage parlors or fast houses, i would assume they want you in and out asap